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I get .837 inches with those dimensions at http://diyfishkeepers.com/AcrylicThicknessCalculator.htm
And at this site it does say 3/4" would suffice http://www.cichlid-forum.com/articles/diy_acrylic_aquarium.php
And that was just a quick google search...
Now dont get me wrong the tank looks beautiful and you can see the craftsmanship, but did you deliberately search for "what's the thinnest i can make this?"